Question

The sum of $24$ terms of the following series $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\dots$ is

• A. $300$
• B. $300\sqrt{2}$
• C. $200\sqrt{2}$
• D. none of these

Answer 1

Answer: (B)

$\Sigma n=\frac{n(n+1)}{2}$
We have $\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32}+\dots$
$=1\sqrt{2}+2\sqrt{2}+3\sqrt{2}+4\sqrt{2}+\dots$
$=\sqrt{2}(1+2+3+4+\dots$ upto 24 terms $)$
$=\sqrt{2}\times \frac{24\times 25}{2}$
$=300\sqrt{2}$